共查询到20条相似文献,搜索用时 500 毫秒
1.
Asymptotic behaviors of zero modes of the massless Dirac operator H = α · D + Q(x) are discussed, where α = (α1, α2, α3) is the triple of 4 × 4 Dirac matrices, , and Q(x) = (q
jk
(x)) is a 4 × 4 Hermitian matrix-valued function with | q
jk
(x) | ≤ C 〈x〉−ρ, ρ > 1. We shall show that for every zero mode f, the asymptotic limit of |x|2
f (x) as |x| → + ∞ exists. The limit is expressed in terms of the Dirac matrices and an integral of Q(x) f (x).
相似文献
2.
Vladimir Rabinovich 《Russian Journal of Mathematical Physics》2012,19(1):107-120
The propagation of electromagnetic waves issued by modulated moving sources of the form j( t,x ) = a( t )e - iw0 t [(x)\dot]0 ( t )d( x - x0 ( t ) )j\left( {t,x} \right) = a\left( t \right)e^{ - i\omega _0 t} \dot x_0 \left( t \right)\delta \left( {x - x_0 \left( t \right)} \right) is considered, where j(t, x) stands for the current density vector, x = (x
1, x
2, x
3) ∈ ℝ3 for the space variables, t ∈ ℝ for time, t → x
0(t) ∈ ℝ3 for the vector function defining the motion of the source, ω
0 for the eigenfrequency of the source, a(t) for a narrow-band amplitude, and δ for the standard δ function. Suppose that the media under consideration are dispersive. This means that the electric and magnetic permittivity
ɛ(ω), μ(ω) depends on the frequency ω. We obtain a representation of electromagnetic fields in the form of time-frequency oscillating integrals whose phase contains
a large parameter λ > 0 characterizing the slowness of the change of the amplitude a(t) and the velocity [(x)\dot]0 ( t )\dot x_0 \left( t \right) and a large distance between positions of the source and the receiver. Applying the two-dimensional stationary phase method
to the integrals, we obtain explicit formulas for the electromagnetic field and for the Doppler effects. As an application
of our approach, we consider the propagation of electromagnetic waves produced by moving source in a cold nonmagnetized plasma
and the Cherenkov radiation in dispersive media. 相似文献
3.
The nonadiabatic corrections to the self-energy part Σs(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no
direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response
functions and Σs(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σs(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σs(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides
in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence
of a narrow additional line in the phonon spectral function S(q, ω)≈−π
−1 Im D
s
(q, ω), where D
s
(q, ω) is the phonon Green’s function, at temperatures T<T
c
.
Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999) 相似文献
4.
A. Fledderjohann A. Klümper K.-H. Mütter 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,72(4):559-565
The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins
S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix ΔS
(n+1) of 4 neighbouring “n clusters” of size 2n × 2n, n = 1,2,3,... from the corresponding quantities ΔS
(n). Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies
ES
(n+1), S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices
are generated by the transitions 〈S’,m’;n+1|Sq
*|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2n+1 × 2n+1, mediated by the staggered spin operator Sq
*. 相似文献
5.
6.
Sadataka Furui 《Few-Body Systems》2009,46(1):73-74
We calculate the propagator of the domain wall fermion (DWF) of the RBC/UKQCD collaboration with 2 + 1 dynamical flavors of
163 × 32 × 16 lattice in Coulomb gauge, by applying the conjugate gradient method. We find that the fluctuation of the propagator
is small when the momenta are taken along the diagonal of the 4-dimensional lattice. Restricting momenta in this momentum
region, which is called the cylinder cut, we compare the mass function and the running coupling of the quark-gluon coupling
α
s,g1(q) with those of the staggered fermion of the MILC collaboration in Landau gauge. In the case of DWF, the ambiguity of the
phase of the wave function is adjusted such that the overlap of the solution of the conjugate gradient method and the plane
wave at the source becomes real. The quark-gluon coupling α
s,g1(q) of the DWF in the region q > 1.3 GeV agrees with ghost-gluon coupling α
s
(q) that we measured by using the configuration of the MILC collaboration, i.e., enhancement by a factor (1 + c/q
2) with c ≃ 2.8 GeV2 on the pQCD result. In the case of staggered fermion, in contrast to the ghost-gluon coupling α
s
(q) in Landau gauge which showed infrared suppression, the quark-gluon coupling α
s,g1(q) in the infrared region increases monotonically as q→ 0. Above 2 GeV, the quark-gluon coupling α
s,g1(q) of staggered fermion calculated by naive crossing becomes smaller than that of DWF, probably due to the complex phase of
the propagator which is not connected with the low energy physics of the fermion taste.
An erratum to this article can be found at 相似文献
7.
A. S. Demidov 《Russian Journal of Mathematical Physics》2010,17(2):145-153
For a given domain ω ⋐ ℝ2 with boundary γ = ∂ω, we study the cardinality of the set $
\mathfrak{A}_\eta \left( \Phi \right)
$
\mathfrak{A}_\eta \left( \Phi \right)
of pairs of numbers (a, b) for which there is a function u = u
(a,b): ω → ℝ such that ∇2
u(x) = au(x) + b ⩾ 0 for x ∈ ω, u|
γ
= 0, and ||∇u(s)| − Φ(s) ⩽ η for s ∈ γ. Here η ⩾ 0 stands for a very small number, Φ(s) = |∇(s)| / ∫
γ
|∇v| d
γ, and v is the solution of the problem ∇2
v = a
0
v + 1 ⩾ 0 on ω with v|
γ
= 0, where a
0 is a given number. The fundamental difference between the case η = 0 and the physically meaningful case η > 0 is proved. Namely, for η = 0, the set $
\mathfrak{A}_\eta \left( \Phi \right)
$
\mathfrak{A}_\eta \left( \Phi \right)
contains only one element (a, b) for a broad class of domains ω, and a = a
0. On the contrary, for an arbitrarily small η > 0, there is a sequence of pairs (a
j
, b
j
) ∈ $
\mathfrak{A}_\eta \left( \Phi \right)
$
\mathfrak{A}_\eta \left( \Phi \right)
and the corresponding functions u
j
such that ‖f
u
j+1‖ − ‖f
u
j
‖ > 1, where ‖f
u
j
= max
x∈ω
|f
u
j
(x)| and f
u
j
(x) = a
j
u
j
(x) + b
j
. Here the mappings f
u
j
: ω → ℝ necessarily tend as j → ∞ to the δ-function concentrated on γ. 相似文献
8.
Extensions of Lieb’s Concavity Theorem 总被引:3,自引:1,他引:2
Frank Hansen 《Journal of statistical physics》2006,124(1):87-101
The operator function (A,B)→ Trf(A,B)(K
*)K, defined in pairs of bounded self-adjoint operators in the domain of a function f of two real variables, is convex for every Hilbert Schmidt operator K, if and only if f is operator convex. We obtain, as a special case, a new proof of Lieb’s concavity theorem for the function (A,B)→ TrA
p
K
*
B
q
K, where p and q are non-negative numbers with sum p+q ≤ 1. In addition, we prove concavity of the operator function
in its natural domain D
2(μ1,μ2), cf. Definition 3. 相似文献
9.
F. Rahaman Peter K. F. Kuhfittig K. Chakraborty M. Kalam D. Hossain 《International Journal of Theoretical Physics》2011,50(9):2655-2665
This paper discusses a new model for galactic dark matter by combining an anisotropic pressure field corresponding to normal
matter and a quintessence dark energy field having a characteristic parameter ω
q
such that
-1 < wq < -\frac13-1<\omega_{q}< -\frac{1}{3}. Stable stellar orbits together with an attractive gravity exist only if ω
q
is extremely close to
-\frac13-\frac{1}{3}, a result consistent with the special case studied by Guzman et al. (Rev. Mex. Fis. 49:303, 2003). Less exceptional forms of quintessence dark energy do not yield the desired stable orbits and are therefore unsuitable
for modeling dark matter. 相似文献
10.
This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order
operators on the half-line is developed, and the trace inequality
tr( (-D)2 - CHRd,2\frac1|x|4 - V(x) )-g £ Cgò\mathbbRd V(x)+g+ \fracd4 dx, g 3 1 - \frac d 4,\mathrm{tr}\left( (-\Delta)^2 - C^{\mathrm{HR}}_{d,2}\frac{1}{|x|^4} - V(x) \right)_-^{\gamma}\leq C_\gamma\int\limits_{\mathbb{R}^d} V(x)_+^{\gamma + \frac{d}{4}}\,\mathrm{d}x, \quad \gamma \geq 1 - \frac d 4, 相似文献
11.
12.
The dynamic structure factor S(q, ω) of a harmonically trapped Bose gas has been calculated well above the Bose-Einstein condensation temperature by treating
the gas cloud as a canonical ensemble of non-interacting classical particles. The static structure factor is found to vanish
s8 q
2 in the long-wavelength limit. We also incorporate a relaxation mechanism phenomenologically by including a stochastic friction
force to study S(q, ω). A significant temperature dependence of the density fluctuation spectra is found. The Debye-Waller factor has been calculated
for the trapped thermal cloud as a function of q and the number N of atoms. A substantial difference is found for small- and large-N clouds. 相似文献
13.
Anna Maltsev 《Communications in Mathematical Physics》2010,298(2):461-484
We extend some recent results of Lubinsky, Levin, Simon, and Totik from measures with compact support to spectral measures of Schrödinger operators on the half-line. In particular, we define a reproducing kernel S L for Schrödinger operators and we use it to study the fine spacing of eigenvalues in a box of the half-line Schrödinger operator with perturbed periodic potential. We show that if solutions u(ξ, x) are bounded in x by ${e^{\epsilon x}}
|